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Rahimkhani, Parisa, Sabermahani, Sedigheh, Abdeljawad, Thabet. (1405). Numerical simulation of nonlinear Galilei invariant advection–diffusion equations via fractal–fractional operators. فیزیولوژی و بیوتکنولوژی آبزیان, (), -. doi: 10.22124/jmm.2026.32909.2994
Parisa Rahimkhani; Sedigheh Sabermahani; Thabet Abdeljawad. "Numerical simulation of nonlinear Galilei invariant advection–diffusion equations via fractal–fractional operators". فیزیولوژی و بیوتکنولوژی آبزیان, , , 1405, -. doi: 10.22124/jmm.2026.32909.2994
Rahimkhani, Parisa, Sabermahani, Sedigheh, Abdeljawad, Thabet. (1405). 'Numerical simulation of nonlinear Galilei invariant advection–diffusion equations via fractal–fractional operators', فیزیولوژی و بیوتکنولوژی آبزیان, (), pp. -. doi: 10.22124/jmm.2026.32909.2994
Rahimkhani, Parisa, Sabermahani, Sedigheh, Abdeljawad, Thabet. Numerical simulation of nonlinear Galilei invariant advection–diffusion equations via fractal–fractional operators. فیزیولوژی و بیوتکنولوژی آبزیان, 1405; (): -. doi: 10.22124/jmm.2026.32909.2994

Numerical simulation of nonlinear Galilei invariant advection–diffusion equations via fractal–fractional operators

Journal of Mathematical Modeling
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 09 مرداد 1405
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.22124/jmm.2026.32909.2994
نویسندگان
Parisa Rahimkhani* 1؛ Sedigheh Sabermahani2؛ Thabet Abdeljawad3
1Faculty of Science, Mahallat Institute of Higher Education, Mahallat, Iran
2Department of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, Iran
3Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833,11586 Riyadh, Saudi Arabia
چکیده
In this paper, a new class of fractal-fractional differential equations called the fractal

fractional Galilei invariant advection–diffusion equation is introduced for the first time. Then,

we introduce a method based on the fractional Genocchi functions for solving this problem.

To achieve the stated objective, we first derive the fractal-fractional and integer-order integral operators for the fractional Genocchi functions in the Atangana-Riemann-Liouville sense.

Then, the obtained integral operators of the fractional Genocchi functions, along with certain properties of the fractional Genocchi functions, are utilized within a collocation method

to reduce the fractal-fractional Galilei invariant advection- diffusion equation to a system of

algebraic equations involving the unknown coefficients. Finally, the convergence analysis of

the proposed method is examined in the Sobolev space. In addition, illustrative examples are

provided to demonstrate the validity and applicability of the proposed method.
کلیدواژه‌ها
Fractal-fractional nonlinear Galilei invariant advection–diffusion equations؛ Fractional Genocchi functions؛ Fractal-fractional integral operators؛ Convergence analysis
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تعداد مشاهده مقاله: 5


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